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Simplifying 4x2 + -17x + 9 = 0 Reorder the terms: 9 + -17x + 4x2 = 0 Solving 9 + -17x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -4.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -4.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -4.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -4.25x + x2 = 0 + -2.25 -4.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -4.25x + x2 = -2.25 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -2.25 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -2.25 + 4.515625 Combine like terms: -2.25 + 4.515625 = 2.265625 4.515625 + -4.25x + x2 = 2.265625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + -2.125) equal to 1.505199322 and -1.505199322.Subproblem 1
x + -2.125 = 1.505199322 Simplifying x + -2.125 = 1.505199322 Reorder the terms: -2.125 + x = 1.505199322 Solving -2.125 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.505199322 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.505199322 + 2.125 x = 1.505199322 + 2.125 Combine like terms: 1.505199322 + 2.125 = 3.630199322 x = 3.630199322 Simplifying x = 3.630199322Subproblem 2
x + -2.125 = -1.505199322 Simplifying x + -2.125 = -1.505199322 Reorder the terms: -2.125 + x = -1.505199322 Solving -2.125 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.505199322 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.505199322 + 2.125 x = -1.505199322 + 2.125 Combine like terms: -1.505199322 + 2.125 = 0.619800678 x = 0.619800678 Simplifying x = 0.619800678Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.630199322, 0.619800678}
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